## Wednesday, August 9, 2017

### Multiple Regression Explained

How to interpret multiple regression

Regression is useful for making a predictive model. Let's say there's a positive linear correlation between K and N, but you suspect that Factors L and M also contribute to Outcome N

Make up a storysay, that Factors K, L, and M represent intelligence, persistence, and amount of sleep per night and N refers to a course grade.

So, to test the relative impacts of Factors K, L, and M on Outcome N, you can feed each factor into a regression model, and test whether each factor increases the fit. That is, a correlation between Factor K and Outcome N yields a Pearson's r of .64 and R2 of .4096.

But, when you run a regression testing the effect of Factors K and L on Outcome N, you find an R2 of .5625, with a significant change in the R2 value. That means that Factors K and L together do a better job of explaining the relationship than Factor K alone.

Then, you run a regression with Factors K, L, and M together, and find an R2 of .5929, with no significant changethis means that Factor M does not help to explain the relationship. Outcome N is due mostly to Factors K and L; Factor M is an unimportant predictor of Outcome N.

VoilĂ ! There's regression in a nutshell!

And, if you're confused about the math...remember in middle school or high school math, when you learned about "rise over run" and learned the formula y = mx + b? Yeah, that's a simple linear regression. With multiple regression, you can add multiple terms, such that y = ax1 + bx2 + cx3...+ z. But it's still the same concept, just with more predictors than that lone "mx" term.

In case you missed it, there are some fantastic, easy-to-use, and FREE stats programs available now! I review them here.
For more help explaining statistical concepts and when to use them,